Cole picked up a hamstring injury in the first half of his side's FA Cup quarter-final win over Manchester United and is expected to be out for up to two weeks.
Chelsea face Rubin Kazan in the Europa League, Sunderland in the Premier League and Manchester City in the FA Cup over that period and Bertrand is keen to take his chance.
|6/4||Chelsea are 6/4 to win the FA Cup with Coral|
"Rubin have done really well and managed to knock out the holders in the round of 32. They've had very good away form so I'm sure they'll give us some tough competition.
The former England Under-21 international believes he can gain enough experience in the next few weeks to later push Cole as first-choice left-back.
"It's down to me to keep training well, keep my performances up to a level and keep pushing and pushing until the time comes," he said.
"He's been a focal point for my career even before he was at Chelsea. He was someone I used to watch when I was younger and having him here at Chelsea has been a good chance for me to see first-hand how he goes about his work day in, day out and he provided a good basis for me to plan around."
Despite having already won the Champions League in his young career, Bertrand says he is still keen to get his hands on the Europa League trophy.
"It's a chance to get another fantastic trophy if we do go all the way and win it," he added. "To have a chance to be in any competition at my age is a fantastic thing."